Quantum Howe duality and invariant polynomials

We construct two examples of q-deformed classical Howe dual pairs (sl(2, C), so(3, (C)) and (sl(2, C), sl(n, C)). Moreover, we obtain a noncommutative version of the first fundamental theorem of classical invariant theory. Our approach to these dualities differs from [9] and [11]. Furthermore, we solve the tensor product decomposition problem for Verma modules over U-q(sl(2, C)) provided q is not a root of unity. (C) 2019 Elsevier Inc. All rights reserved.